Secondary currents and very-large-scale motions in open-channel flow over streamwise ridges

It is widely acknowledged that streamwise ridges on the bed of open-channel flows generate secondary currents (SCs). A recent discovery of meandering long streamwise counter-rotating vortices in open-channel flows, known as very-large-scale motions (VLSMs), raises a question regarding the interrelations between VLSMs and SCs in flows over ridge-covered fully rough beds. To address it, we conducted long-duration experiments using stereoscopic particle image velocimetry, covering a range of ridge spacings (s) from approximate to 0.4 to approximate to 4 flow depths (H). For a benchmark no-ridge case, the flow is quasi-two-dimensional in the central part of the channel, exhibiting a strong spectral signature of VLSMs, as expected. With ridges on the bed at s (sic) 2H, two SC cells are formed between neighbouring ridges and VLSMs are entirely suppressed, suggesting that ridge-induced SCs prevent the formation of VLSMs by absorbing their energy or overpowering their formation. At the same time, velocity auto- and cross-spectra reveal a new feature that can be explained by low-amplitude meandering of the alternating low- and high-momentum flow regions associated with instantaneous manifestations of SCs. Two-point velocity correlations and smooth velocity field reconstructions using proper orthogonal decomposition further support the validity of this effect. Its origin is probably due to the instability related to the presence of inflection points in the spanwise distribution of the streamwise velocity within the SC cells. These results have implications for bed friction in open channels, where the friction factor may increase if depth-scale SCs are present, or decrease under conditions of sub-depth-scale SCs and suppressed VLSMs.